Prior work has previously used attempted to use analog circuits, e.g., Laszlo B. Kisch, “Quantum Computing with Analog Circuits: Hilbert Space Computing”, Proceedings of SPIE Vol. 5055 (2003) or signal processing, e.g., B. R. LaCour and G. E. Ott, “Signal-based Classical Emulation of a Universal Quantum Computer”, New Journal of Physics, 17, 2015 to attempt to emulate quantum dynamical systems. However, such systems require the use of a 90°-phase shifter to represent the imaginary number i in quantum mechanics, which is impossible to practically create over an infinite frequency range as is needed. They do not have the capability to automatically represent and efficiently control essential quantum features such as the Planck constant, probability conservation, and energy conservation, important in quantum entanglement and correlated quantum operations. They do not have the capability to or do not efficiently emulate the stochastics or noise of quantum mechanical systems that couples quantum damping and quantum fluctuation, and which is an integral part of quantum uncertainty and some quantum-computing applications. They use other ideal mathematical signal-processing elements that require large numbers of devices to create, making them impractical to implement in actual physical systems or with compact physical circuits built with transistors. They do not provide methods that compensate for loss in actual physical systems such that they can behave in an ideal nearly lossless quantum or quantum-inspired fashion, which is beneficial for both quantum control and for quantum computing and necessary for actual physical emulations. They do not exploit efficient means for probability measurement and probability pattern recognition that are amenable to compact transistor implementations. They do not show how easily-created nonlinear operation in classical systems can create novel hybrid quantum-classical architectures that are useful for both quantum and quantum-inspired computing or for investigation of non-independent particle interactions. Finally, they do not show how a linear scaling in the number of classical circuits can help implicitly represent and initiate an exponential number of quantum tensor-product superposition states, even if they are not all simultaneously accessible as in actual quantum systems.
Given the large numbers of applications of quantum and quantum-inspired systems possible with even the interaction of a modest number of quantum two-state systems, e.g. for novel computing M. Nielsen & I. Chuang, “Quantum Computation and Quantum Information,” Cambridge University Press, 2000, communication, and quantum chemistry, e.g., Ivan Kassal, et. al, “Simulating chemistry using quantum computers.” Annual Review of Physical Chemistry, Vol. 62 pp. 185-207, 2011, as well as the easy availability of large numbers of transistors on current integrated-circuit chips at room temperature, there is both a need and an opportunity for efficient emulation of quantum circuits with classical circuit building blocks. Such emulation can not only be directly useful in applications that classically emulate quantum operation on transistor chips in hardware but it can also help create circuit-based software tools that design and analyze actual synthetic or natural quantum or quantum-inspired systems, e.g, as in Josephson-junction based superconducting quantum systems.